# -*- coding: utf-8 -*-
#
# utils.py - helper functions for community-finding algorithms
#
# Copyright 2011 Ben Edwards <bedwards@cs.unm.edu>.
# Copyright 2011 Aric Hagberg <hagberg@lanl.gov>.
# Copyright 2015 NetworkX developers.
#
# This file is part of NetworkX.
#
# NetworkX is distributed under a BSD license; see LICENSE.txt for more
# information.
"""Helper functions for community-finding algorithms."""


def is_partition(G, communities):
    """Return ``True`` if and only if ``communities`` is a partition of
    the nodes of ``G``.

    A partition of a universe set is a family of pairwise disjoint sets
    whose union is the entire universe set.

    ``G`` is a NetworkX graph.

    ``communities`` is an iterable of sets of nodes of ``G``. This
    iterable will be consumed multiple times during the execution of
    this function.

    """
    # Alternate implementation:
    #
    #     return (len(G) == sum(len(c) for c in community) and
    #             set(G) == set.union(*community))
    #
    return all(sum(1 if v in c else 0 for c in communities) == 1 for v in G)
